Homotopically trivializing the circle in the framed little disks

This paper confirms the following suggestion of Kontsevich. In the appropriate derived sense, an action of the framed little disks operad and a trivialization of the circle action is the same information as an action of the Deligne-Mumford-Knudsen operad. This improves an earlier result of the author and Bruno Vallette.Comment: 36 pages. This version accepted for publication by the Journal of Topolog

An update on domineering on rectangular boards

Domineering is a combinatorial game played on a subset of a rectangular grid between two players. Each board position can be put into one of four outcome classes based on who the winner will be if both players play optimally. In this note, we review previous work, establish the outcome classes for several dimensions of rectangular board, and restrict the outcome class in several more.Comment: 9 pages. References fixe

Peaks and Troughs in Helioseismology: The Power Spectrum of Solar Oscillations

I present a matched-wave asymptotic analysis of the driving of solar oscillations by a general localised source. The analysis provides a simple mathematical description of the asymmetric peaks in the power spectrum in terms of the relative locations of eigenmodes and troughs in the spectral response. It is suggested that the difference in measured phase function between the modes and the troughs in the spectrum will provide a key diagnostic of the source of the oscillations. I also suggest a form for the asymmetric line profiles to be used in the fitting of solar power spectra. Finally I present a comparison between the numerical and asymptotic descriptions of the oscillations. The numerical results bear out the qualitative features suggested by the asymptotic analysis but suggest that numerical calculations of the locations of the troughs will be necessary for a quantitative comparison with the observations.Comment: 18 pages + 8 separate figures. To appear in Ap

Shallow Surveying in Hazardous Waters

Of order one importance to any study of nearshore processes is knowledge of the bathymetry in shallow water. This is true for studies on open coast sandy beaches where surf zone dynamics drive the system, inlet environments where bathymetric evolution can rapidly change navigation channels, and in more benign, lower-energy coastal environments that evolve slowly over 10’s to 100’s of years. Difficulties in obtaining shallow bathymetry where depth-limited wave breaking occurs, submerged hazards are present, or other harsh environments has led to the development of survey systems on highly maneuverable personal watercraft (Beach, et al., 1994; Cote, 1999; Dugan, et al., 1999; MacMahan, 2001). In this work we discuss shallow water surveying from the Coastal Bathymetry Survey System (CBASS), a Yamaha Waverunner equipped with differential GPS, single-beam 192 KHz acoustic echo-sounder, and onboard navigation system. Data obtained with the CBASS in three regions will be discussed, including an energetic surf zone located in southern California during the 2003 Nearshore Canyon Experiment (NCEX), on Lake Erie in 2002 (and compared with historical surveys dating back 150 years), and around Piscataqua River Inlet, NH, in 2007. Estimated accuracy (for sandy bottoms) in water depths ranging 1–10 m are 0.07-0.10 m in the vertical, and on the order of 0.1-1 m horizontally depending on water depth and bottom slope. The high maneuverability of the personal watercraft makes very shallow water bathymetric surveys possible with acoustic altimeters, particularly in regions where airborne remote sensing systems fail (owing to water clarity issues) or where repeated high resolution surveys are required (e.g., where an erodible bottom is rapidly evolving)

A criterion for existence of right-induced model structures

Suppose that $F: \mathcal{N} \to \mathcal{M}$ is a functor whose target is a Quillen model category. We give a succinct sufficient condition for the existence of the right-induced model category structure on $\mathcal{N}$ in the case when $F$ admits both adjoints. We give several examples, including change-of-rings, operad-like structures, and anti-involutive structures on infinity categories. For the last of these, we explore anti-involutive structures for several different models of $(\infty, 1)$-categories, and show that known Quillen equivalences between base model categories lift to equivalences

Airborne Fraunhofer Line Discriminator

Airborne Fraunhofer Line Discriminator enables prospecting for fluorescent materials, hydrography with fluorescent dyes, and plant studies based on fluorescence of chlorophyll. Optical unit design is the coincidence of Fraunhofer lines in the solar spectrum occurring at the characteristic wavelengths of some fluorescent materials